Black hole-neutron star and neutron star-neutron star mergers are extreme astrophysical events powering the emission of observable gravitational wave and electromagnetic (EM) signals. The first observation of gravitational waves by advanced LIGO, from two merging black holes, will soon be followed by the observation of mergers involving neutron stars. Thorough follow-up campaigns will aim to observe any EM counterpart to the gravitational wave signal. The most promising counterparts are probably kilonovae, optical/infrared transients powered by radioactive decays in neutron-rich material ejected by the merger. If properly modeled, kilonovae can tell us about the environment of the merger and the properties of the merging objects. Nucleosynthesis in the ejected material may also be the main source of production of many heavy elements (gold, platinum). Kilonovae will thus help us determine the role of neutron star mergers in the production of these elements. In this talk, I will discuss our current understanding of kilonovae, as well as the complex numerical simulations which are required to model them. I will show that neutrino-matter interactions play a critical role in determining the properties of kilonovae, and will describe efforts to improve neutrino transport schemes in general relativistic simulations of neutron star mergers.